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Related Concept Videos

Stress Concentrations01:24

Stress Concentrations

441
Stress concentration is when stress intensifies near discontinuities such as holes or abrupt cross-sectional changes in a structural member. This localized stress can often surpass the average stress within the member. The stress distribution in flat bars, either with a circular hole or varying widths connected by fillets, can be determined experimentally using a photoelastic method. The results are based on ratios of geometric parameters like the ratio of the hole's radius to the smaller...
441
Stress Concentrations01:13

Stress Concentrations

403
The concept of stress concentration is crucial for understanding how materials respond under bending stresses, particularly when there are irregularities or discontinuities in the material's geometry. Normally, stress in a symmetric member subjected to pure bending is assumed to be uniformly distributed across the entire cross-section. However, this assumption does not hold when there are variations in the cross-sectional geometry or the presence of notches and holes.
The stress...
403
Yield Criteria for Ductile Materials under Plane Stress01:25

Yield Criteria for Ductile Materials under Plane Stress

283
In designing structural elements and machine parts using ductile materials, it is crucial to ensure that these components withstand applied stresses without yielding. Yielding is initially determined through a tensile test, which evaluates the material's response to uniaxial stress. However, tensile stress is insufficient when components face biaxial or plane stress conditions This condition requires advanced criteria to predict failure.
The Maximum Shearing Stress Criterion, also known as...
283
Principal Stresses in a Beam01:11

Principal Stresses in a Beam

489
In prismatic beams subject to arbitrary transverse loading, It is essential to analyze the interaction between shear forces and bending moments in order to understand stress distribution and ensure structural integrity. The highest normal or bending stress occurs at the outer fibers of the beam, decreasing linearly to zero at the neutral axis. In contrast, shear stress peaks at the neutral axis and diminishes toward the outer surfaces.
Analyzing principal stresses is crucial, especially in...
489
Residual Stresses01:26

Residual Stresses

348
Residual stresses reside in a structure even after removing the original stress inducer. This phenomenon often arises from varied plastic deformations across different parts of a structure. Consider a rod stretched beyond its yield point. It will not regain its original length due to permanent deformation. Even after load removal, the rod does not entirely lose stress because of uneven plastic deformations, resulting in residual stresses. The computation of these stresses in structures is...
348
Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

10.5K
The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
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Determining the Mechanical Strength of Ultra-Fine-Grained Metals
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Stress minimization for lattice structures. Part I: Micro-structure design.

A Ferrer1, P Geoffroy-Donders2, G Allaire1

  • 1CMAP, École Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau, France.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|May 24, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a novel super-ellipsoidal hole for lattice structures to minimize stress concentration. This optimized microstructure design enhances material performance in additive manufacturing applications.

Keywords:
homogenizationlattice structureoptimal design

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Area of Science:

  • Materials Science
  • Mechanical Engineering
  • Computational Mechanics

Background:

  • Lattice structures offer an excellent balance of stiffness and low weight, suitable for additive manufacturing.
  • Current lattice optimization primarily focuses on minimizing compliance, not stress.
  • Extending lattice optimization to stress minimization is crucial for advanced material design.

Purpose of the Study:

  • To develop and analyze a new parametrized periodicity cell for 2D lattice optimization focused on stress minimization.
  • To investigate the influence of cell parameters on stress amplification.
  • To establish an optimal microstructure for stress reduction in lattice materials.

Main Methods:

  • Parametrization of a square lattice cell with a super-ellipsoidal hole using an orientation angle, semi-axes, and a corner smoothing parameter.
  • Numerical experiments to analyze the impact of parameters on the stress amplification factor.
  • Optimization of the corner smoothing parameter for various microstructures and macroscopic stresses.

Main Results:

  • The super-ellipsoidal hole design effectively reduces stress concentration compared to standard rectangular holes.
  • Optimal corner smoothing parameters were determined for different stress conditions.
  • Averaging of optimal parameters provides a generalized solution for stress minimization.

Conclusions:

  • The proposed super-ellipsoidal microstructure is a promising approach for stress minimization in lattice structures.
  • This work lays the foundation for 2D lattice optimization in stress-critical applications.
  • The findings contribute to the mathematical design of complex materials with enhanced mechanical properties.